Complete Orbits for Twist Maps on the Plane: Extensions and Applications

Twist maps (θ ₁, r ₁) = f (θ, r) on the plane are considered which do not exhibit any kind of periodicity in their dependence on θ. Some general results are obtained which typically yield the existence of infinitely many complete and bounded orbits. Examples that can be treated with this theory include oscillators of the type (x)\ddot]+V￠(x)=p(t){\ddot{x}+V'(x)=p(t)} under appropriate hypotheses, the bouncing ball system, and the standard map.